We don't have synonyms for shop around yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are shops around, show around and slop around.
(v) :
(intransitive) To actively search and compare options before making a selection or choice of vendor.
(v) :
(intransitive) To actively make a search for an alternative choice of something one has, owns, or wants, without it necessarily involving buying or selling anything.
(v) :
(transitive) To put something out on offer to multiple parties in the hope one will choose it.
(v) :
(intransitive) To actively search and compare options before making a selection or choice of vendor.
(v) :
(intransitive) To actively make a search for an alternative choice of something one has, owns, or wants, without it necessarily involving buying or selling anything.
(v) :
(transitive) To put something out on offer to multiple parties in the hope one will choose it.